Power distribution network robust voltage optimization regulation and control method based on stable partitioning and alternate iteration

Abstract

The invention discloses a power distribution network robust voltage optimization regulation and control method based on stable partitioning and alternate iteration, belongs to the technical field of active power distribution network distributed optimization control, and solves the problems that a partitioning result is prone to instability and boundary coordination efficiency is low under high-proportion photovoltaic access. Rapid coordination of the whole network is realized in combination with double-layer alternate iteration of virtual nodes, photovoltaic output uncertainty is represented by adopting a Gaussian mixture model, and a comprehensive electrical distance is constructed by using a voltage sensitivity distance and Kullback-Leibler divergence; forming a stable partition structure by using a density peak clustering algorithm; a linearization optimization model with minimum voltage deviation and network loss as targets is established, inter-partition power coupling modeling is realized by setting virtual nodes, distributed convergence is realized by adopting an alternate iterative algorithm of outer layer boundary coordination and inner layer partition solution, and the robustness and coordination convergence speed of a partition structure are remarkably improved.

Description

Technical Field

[0001] This invention belongs to the field of distributed optimization control technology for active distribution networks, and relates to a robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration. Background Technology

[0002] In recent years, with the rapid development of distributed photovoltaic (PV) power generation technology, a large number of PV power sources have been connected to medium- and low-voltage distribution networks. While improving the utilization rate of green energy, the high proportion of PV connections has also significantly altered the power flow distribution and node voltage characteristics of the distribution network, making the network operation highly random, nonlinear, and uncertain. Especially under conditions of rapid changes in solar irradiance and ambient temperature, PV output can fluctuate drastically in a short period, leading to frequent node voltage overshoots and even voltage reversals, posing a threat to the safe and stable operation of the power grid.

[0003] To address voltage fluctuations caused by random photovoltaic (PV) output, traditional power systems commonly employ centralized automatic voltage control (AVC) strategies. Centralized AVC achieves global voltage control by centrally scheduling reactive power compensation devices, transformer tap changes, and inverter reactive power output through a master station. However, with the rapid increase in the number of distributed power sources, the large number of nodes, and limited communication bandwidth in distribution networks, centralized AVC suffers from the following prominent problems: 1) High dependence on communication systems; control performance significantly degrades if communication is delayed or interrupted; 2) Huge computational load for unified optimization across the entire network, poor real-time performance, and inability to meet rapid response requirements; 3) When system topology changes or PV power surges, the centralized control center is prone to frequent recalculation, affecting system stability.

[0004] To overcome the drawbacks of centralized control, researchers have proposed distributed and zoned voltage optimization methods in recent years. These methods divide the distribution network into multiple sub-zones, with each zone independently optimizing voltage and reactive power, thereby reducing global communication. Existing zoning methods primarily use line impedance, electrical distance, or sensitivity matrices for partitioning. For example, impedance-distance-based zoning methods can reflect topological electrical characteristics well, but they struggle to capture the dynamic impact of photovoltaic (PV) output disturbances on voltage. Sensitivity-based zoning methods can yield reasonable results under static conditions, but when PV output fluctuates drastically, the sensitivity matrix changes with the operating point, leading to frequent reconfiguration of the zoning results. These methods are poorly adapted to high-penetration PV scenarios in distribution networks with strong randomness and variable operating points, and their zoning structure lacks stability.

[0005] Furthermore, existing distributed optimization algorithms are generally based on ADMM (Alternating Direction Multiplier Method) or subgradient iteration methods to achieve inter-region coordination. Although these methods can theoretically achieve global convergence, they still have the following problems in engineering applications: 1) The power flow equations are non-convex, and the algorithm is prone to getting trapped in local optima or oscillating convergence; 2) The boundary voltage coupling relationship between regions is not fully modeled, resulting in frequent information exchange and slow convergence speed; 3) When changes in photovoltaic output cause the system state to deviate from the design point, the iteration process may diverge, resulting in poor robustness.

[0006] Therefore, existing technologies still face the following technical bottlenecks under conditions of high photovoltaic grid connection: the partitioned structure is sensitive to uncertain disturbances and has poor stability; the boundary coordination mechanism is incomplete and the optimization solution process is not robust enough; centralized control has a slow response and distributed algorithms have low convergence efficiency.

[0007] In summary, existing technologies struggle to balance regional stability, optimized efficiency, and overall grid coordination under fluctuating photovoltaic output conditions. Therefore, a robust voltage optimization and control method for distribution networks based on stable regionalization and alternating iteration is urgently needed. Summary of the Invention

[0008] The technical solution of this invention is used to solve the problems of unstable zoning results and low boundary coordination efficiency under high proportion of photovoltaic access.

[0009] The present invention solves the above-mentioned technical problems through the following technical solutions: This invention provides a robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration, comprising the following steps: S1. Collect power grid operating parameters and establish a node topology matrix as input for voltage sensitivity and power flow Jacobian matrix calculation; S2. Based on historical photovoltaic power samples, a photovoltaic power output probability density model is established using a multidimensional Gaussian mixture model. The model parameters are solved iteratively using the expectation-maximization algorithm. The objective function is the log-likelihood function. When the log-likelihood function converges, the parameter estimation is completed. The optimal number of mixture components is determined using the Bayesian information criterion. S3. Based on the power flow equation of the distribution network, establish the power flow Jacobian matrix, extract the voltage sensitivity sub-matrix, calculate the sensitivity distance between nodes, use Kullback-Leibler divergence to measure the statistical difference of node voltage distribution, and weight and fuse the sensitivity distance between nodes and the statistical difference of node voltage distribution to obtain the comprehensive electrical distance. S4. Using the node comprehensive electrical distance as input, the density peak clustering algorithm is used to calculate the node local density; the minimum distance from each node to a node with a higher density is calculated; the node comprehensive index is calculated based on the node local density and the minimum distance from each node to a node with a higher density; the node with the largest comprehensive index is selected as the partition center; the remaining nodes are assigned to the corresponding center node according to the minimum distance principle, thus forming a robust and stable partition. S5. Establish a joint objective function for minimizing voltage deviation and network loss within each partition. Combining node power flow balance constraints with voltage and power constraints, linearize the power flow equations using the LinDistFlow model, then substitute them into the joint objective function for minimizing voltage deviation and network loss to obtain the optimal power allocation under fixed boundary conditions. S6. Set up virtual nodes at the boundary nodes of the partitions, calculate the injected power of the virtual nodes, and set boundary voltage coordination constraints between adjacent partitions to form the power-voltage coordination equation of the virtual nodes, thus transforming the power exchange relationship between partitions into a controllable variable form. S7. During the iterative process, under the condition of fixed virtual node voltage, solve the objective function of jointly minimizing voltage deviation and network loss to obtain the optimal power allocation for each partition; then correct the virtual node voltage according to the voltage difference between adjacent partitions. When the virtual node voltage converges to the optimal voltage, the coordinated control of the entire network is realized.

[0010] Furthermore, the formula for establishing the photovoltaic power output probability density model using a multidimensional Gaussian mixture model in step S2 is as follows:

[0011] in, Let M be the probability density function of photovoltaic power, and M be the number of mixed components; The weight of the m-th Gaussian component. and Let be the mean and covariance matrix of the m-th component, respectively, and satisfy . , It is a normal distribution function; The formula for the log-likelihood function is as follows:

[0012] in, Here is the parameter set of the multidimensional Gaussian mixture model, and k is the number of iterations. These are the parameters of the multidimensional Gaussian mixture model at the (k+1)th iteration. Here are the parameters of the multidimensional Gaussian mixture model at the k-th iteration, and n is the number of samples. For the i-th photovoltaic sample; The formula for determining the optimal number of mixture components using the Bayesian information criterion is as follows:

[0013] in, Let L be the optimal number of mixture components, L be the maximum likelihood estimate, and n be the sample size.

[0014] Furthermore, the voltage sensitivity sub-matrix mentioned in step S3 is as follows:

[0015] in, Let be the sensitivity of the reactive power at node j to the voltage at node i. Let be the voltage magnitude at node i. The amount of reactive power injected into node j; The sensitivity distance between the nodes is:

[0016] in, The sensitivity distance between nodes i and j. Let be the self-sensitivity of node i. Let be the interaction sensitivity of node j with node i; The formula for using Kullback-Leibler divergence to measure the statistical dissimilarity of nodal voltage distribution is as follows:

[0017] in, The statistical difference in voltage distribution at nodes i and j. and Let i and j be the voltage probability distributions for nodes i and j, respectively.

[0018] Furthermore, the formula for obtaining the comprehensive electrical distance by weighting and fusing the inter-node sensitivity distance and the statistical difference in node voltage distribution as described in step S3 is as follows:

[0019] in, For comprehensive electrical distance, All are weighted coefficients.

[0020] Furthermore, the formula for calculating the local density of nodes using the density peak clustering algorithm in step S4 is as follows:

[0021] in, Let be the local density of node i; This is the cutoff distance parameter; The formula for calculating the minimum distance from each node to nodes with a higher density is as follows:

[0022] in, Let be the distance from node i to the nearest node with a higher density than its own. Let be the local density of node j; The formula for calculating the node comprehensive index is as follows:

[0023] in, This is a comprehensive indicator for nodes.

[0024] Furthermore, the objective function for jointly minimizing voltage deviation and network loss in step S5 is as follows:

[0025] in, Let the objective function be the one for the k-th partition. For reference voltage, Let i be the voltage at node i. For reference voltage, These are the weighting coefficients. For branch resistance, For branch current, A robust and stable set of partitions; The node power flow balance constraint is:

[0026] in, and These represent the active and reactive power injections at node i, respectively. Let i be the set of nodes connected to node i. , Let be the voltage vectors at nodes i and j. For branch admittance; This represents the complex conjugate operation. Represents the imaginary unit; The voltage and power constraints are as follows:

[0027] in, Let be the minimum threshold voltage at node i. The maximum threshold voltage at node i. Inject a minimum threshold into the reactive power of node i. Inject the maximum threshold for reactive power at node i; The power flow equations are linearized using the LinDistFlow model to obtain the following:

[0028] in, Let be the active power of branch ij. Let be the reactive power of branch ij. Let be the reactance of branch ij.

[0029] Furthermore, the power-voltage coordination equations for the virtual node in step S6 include: Virtual Node The injection power is:

[0030] in, and These represent the active and reactive power entering the partition, respectively. and These represent the active and reactive power of the outflowing zone, respectively. The boundary voltage coordination constraints between adjacent partitions are:

[0031] in, and These are the virtual boundary node voltages of adjacent partitions p and q, respectively. This is the boundary voltage error limit.

[0032] Furthermore, the formula for correcting the virtual node voltage based on the voltage difference between adjacent intervals in step S7 is as follows:

[0033] In the formula, t is the number of iterations. Step size factor The voltage difference between adjacent partition boundaries. Let be the virtual node voltage at the t-th iteration. This represents the virtual node voltage at the (t+1)th iteration.

[0034] The present invention also provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the above-described robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration, and the processor is configured to execute the program stored in the memory.

[0035] The present invention also provides a storage medium storing a computer program, which, when run by a processor, executes the steps of the above-described robust voltage optimization and control method for distribution networks based on stable partitioning and alternating iteration.

[0036] The beneficial effects of this invention are as follows: This invention integrates the stochastic distribution characteristics of photovoltaic (PV) output with the electrical sensitivity characteristics of nodes to achieve robust and stable partitioning. It combines a virtual node-based two-layer alternating iterative optimization mechanism to achieve rapid network-wide coordination. A Gaussian mixture model (GMM) is used to characterize PV output uncertainty, and a comprehensive electrical distance matrix is ​​constructed using voltage sensitivity distance and Kullback-Leibler divergence. A density peak clustering algorithm is used to form an adaptive and stable partitioning structure under PV fluctuations. Based on this, a linearized optimization model is established with the goal of minimizing voltage deviation and network loss. Virtual nodes are used to model inter-partition power coupling, and an alternating iterative algorithm of outer boundary coordination and inner partitioning solution is employed to achieve distributed convergence. This invention enables rapid voltage optimization control under low communication conditions, significantly improving the robustness, coordination convergence speed, and online control performance of the partitioning structure. It is suitable for medium- and low-voltage active distribution networks with a high proportion of distributed PV access, and can achieve autonomous optimization of partitions and coordinated voltage control across the entire network under the consideration of PV output fluctuations and communication constraints. Attached Figure Description

[0037] Figure 1 This is a flowchart of the robust voltage optimization and control method for distribution networks based on stable partitioning and alternating iteration according to Embodiment 1 of the present invention; Figure 2 A comparison of robust voltage distribution between the robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration in Embodiment 1 of the present invention and the traditional local control method; Figure 3 The convergence curve of the alternating iteration process in the robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration in Embodiment 1 of the present invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below in conjunction with the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] The technical solution of the present invention will be further described below with reference to the accompanying drawings and specific embodiments: Example 1 like Figure 1 As shown, this embodiment of the invention provides a robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration, comprising the following steps: Step 1: Collect power grid operating parameters and establish a node topology matrix. Periodically collect power distribution network operating parameters, including node voltage, current, line impedance, load power, and photovoltaic output data. The sampling period is typically set to 1–5 seconds and can be adaptively adjusted according to photovoltaic fluctuation frequency. The collected data undergoes wavelet thresholding for denoising and moving average smoothing to remove outliers before establishing a node topology matrix. This matrix is ​​used to represent the connection relationship between nodes in the distribution network, to characterize the network structure of the distribution network, and to serve as the structural input for subsequent voltage sensitivity and power flow Jacobian matrix calculations.

[0040] The node topology matrix The formula is as follows: (1) Step 2: Photovoltaic power output probability modeling To describe the randomness and uncertainty of photovoltaic power, a photovoltaic output probability density model is established using a multidimensional Gaussian mixture model (GMM) based on historical photovoltaic power samples, as follows: (2) in, Let M be the probability density function of photovoltaic power, and M be the number of mixed components; The weight of the m-th Gaussian component. and Let be the mean and covariance matrix of the m-th component, respectively, and satisfy . , It is a normal distribution function.

[0041] The model parameters are solved iteratively using the Expectation-Maximization (EM) algorithm, with the objective function being the log-likelihood function, the formula of which is as follows: (3) in, Here is the set of parameters for the GMM model, and k is the number of iterations. These are the parameters of the GMM model at the (k+1)th iteration. Here are the parameters of the GMM model at the k-th iteration, and n is the number of samples. Let i be the i-th photovoltaic sample.

[0042] According to formula (3), parameter estimation is completed when the log-likelihood function converges.

[0043] To avoid overfitting, the Bayesian information criterion is used to determine the optimal number of mixture components, as shown in the following formula: (4) in, The optimal number of mixed components is given by formula (4), where L is the maximum likelihood estimate and n is the sample size. The probability expression of formula (2) combined with formula (4) determines the optimal statistical description of the uncertainty of photovoltaic power output.

[0044] Step 3: Calculation of comprehensive electrical distance between nodes The power flow Jacobian matrix J is established based on the power flow equation of the distribution network, and the voltage sensitivity submatrix is ​​extracted from it.

[0045] The power flow equations of the distribution network are as follows: (5) (6) In the formula, , For nodes Injected active and reactive power; , For nodes and nodes The voltage amplitude; , For nodes , Conductance and susceptance of the admittance matrix between branches; It is a node With nodes The voltage phase angle difference between them For nodes The set of connected adjacent nodes.

[0046] The voltage sensitivity sub-matrix is ​​as follows: (7) in, Let be the sensitivity of the reactive power at node j to the voltage at node i. Let be the voltage magnitude at node i. This represents the amount of reactive power injected into node j.

[0047] The sensitivity distance between nodes is: (8) in, The sensitivity distance between nodes i and j. Let be the self-sensitivity of node i. Let be the interaction sensitivity of node j to node i.

[0048] The sensitivity distance between nodes reflects the static electrical coupling strength between them. However, fluctuations in photovoltaic (PV) output cause dynamic differences in node voltages, so the distance calculated solely based on sensitivity cannot fully reflect the system state. Therefore, this invention introduces the random distribution characteristics of PV output and calculates the node voltage probability distribution function using a PV output probability model. .

[0049] To characterize the impact of photovoltaic output uncertainty on voltage distribution, the statistical dissimilarity of node voltage distribution is measured using the Kullback-Leibler divergence measure, with the specific formula as follows: (9) in, The statistical difference in voltage distribution at nodes i and j. and Let i and j be the voltage probability distributions for nodes i and j, respectively.

[0050] The combined electrical distance is obtained by weighted fusion of formulas (8) and (9): (10) in, For comprehensive electrical distance, All are weighted coefficients, and Both adjust adaptively based on photovoltaic penetration rate; when photovoltaic penetration rate is high, the adjustment is increased. Weights are added to enhance sensitivity to random perturbation characteristics; Formula (10) reflects the combined characteristics of electrical coupling and statistical disturbance. According to the matrix of formula (10) This serves as the input for subsequent stable partitioning algorithms.

[0051] Step 4: Stable partition generation Using the overall electrical distance between nodes as input, the density peak clustering (DPC) algorithm is employed to calculate the local node density; the formula for calculating the local node density is as follows: (11) in, Let be the local density of node i; This is the truncation distance parameter, used to control the cluster radius.

[0052] The minimum distance from each node to nodes with higher density is calculated as follows: (12) in, Let be the distance from node i to the nearest node with a higher density than its own. Let be the local density of node j.

[0053] Comprehensive metrics for computing nodes: (13) in, As a comprehensive indicator for nodes; The largest node is selected as the partition center, and the remaining nodes are assigned to the corresponding center node according to the principle of minimum distance, thus forming a robust and stable partition set. This set is found by searching the matrix. This allows us to determine which branches connect to nodes belonging to different partitions.

[0054] As can be seen from formulas (11) to (12), the local node density measures the degree of node concentration, and the minimum distance ensures the spatial independence of the partition. The combination of the two can realize a stable partition structure under photovoltaic fluctuations. This method is different from the traditional static partitioning based on impedance or sensitivity. It can dynamically maintain the stability of the partition boundary according to photovoltaic fluctuations, which significantly improves the robustness of control.

[0055] This embodiment integrates voltage sensitivity distance and random distribution differences of photovoltaic power output through a comprehensive electrical distance model. It uses density peak clustering algorithm to generate a stable partition structure, so that the partitioning results remain robust under photovoltaic power output disturbances, avoid frequent re-partitioning, and improve the system's operational stability.

[0056] Step 5: Intra-partition optimization modeling In each partition The objective function for jointly minimizing voltage deviation and network loss is established as follows: (14) in, Let the objective function be the one for the k-th partition. For reference voltage, Let i be the voltage at node i. For reference voltage, This is the weighting coefficient, typically ranging from 0.5 to 2. For branch resistance, This represents the branch current.

[0057] The node power flow balance constraint is: (15) in, and These represent the active and reactive power injections at node i, respectively. Let i be the set of nodes connected to node i. , Let be the voltage vectors (including magnitude and phase angle) of nodes i and j. For branch admittance; This represents the complex conjugate operation. It represents the imaginary unit.

[0058] The voltage and power constraints are as follows: (16) in, Let be the minimum threshold voltage at node i. The maximum threshold voltage at node i. Inject a minimum threshold into the reactive power of node i. Inject the maximum threshold for reactive power at node i.

[0059] To simplify the solution, the power flow equations are linearized, relying on the node matrix established in step 1. The LinDistFlow model is constructed as follows: (17) in, Let be the active power of branch ij. Let be the reactive power of branch ij. Let be the reactance of branch ij. Substituting equation (17) into the objective function equation (14) can transform the original non-convex problem into a second-order cone programming (SOCP) form, thereby improving computational convergence. By solving the problem using the interior point method, the solution speed can be significantly improved while ensuring accuracy. The result of the optimization within the partition is the optimal power allocation under fixed boundary conditions.

[0060] This embodiment transforms the non-convex power flow optimization problem within a partition into a second-order cone programming (SOCP) form through LinDistFlow linearization. It establishes power and voltage coordination constraints by setting virtual nodes at the partition boundary nodes and adopts an alternating iterative mechanism of outer boundary coordination and inner partition solution to achieve distributed fast convergence and reduce communication volume and computational complexity.

[0061] Step 6: Virtual Node Boundary Coordination Modeling To handle the power and voltage coupling between different zones, virtual nodes are set at the zone boundary nodes. Virtual nodes The injection power is: (18) in, and These represent the active and reactive power entering the partition, respectively. and These represent the active and reactive power of the outflowing zone, respectively.

[0062] The boundary voltage coordination constraints between adjacent partitions are: (19) in, and These are the virtual boundary node voltages of adjacent partitions p and q, respectively. The boundary voltage error limit is typically set to 0.001–0.005 pu.

[0063] The power-voltage coordination equations of the virtual nodes are formed by formulas (18) and (19), which transform the power exchange relationship between the partitions into a controllable variable form, thus ensuring the coupling coordination between different partitions.

[0064] Step 7: Alternating Iterative Optimization Alternating iterative optimization includes two levels of loops: outer virtual node update and inner partition optimization. The outer loop uses virtual node voltage as the coordination variable, while the inner loop uses the optimal power of the partition as the optimization variable.

[0065] In the i-th iteration, under the condition of fixed virtual node voltage, the objective function of jointly minimizing voltage deviation and network loss is solved to obtain the optimal power allocation for each partition. Then, the virtual node voltage is corrected based on the voltage difference between adjacent intervals: (20) In the formula, t is the number of iterations. This is the step size factor, ranging from 0.1 to 0.5; The voltage difference between adjacent partition boundaries. Let be the virtual node voltage at the t-th iteration. This represents the virtual node voltage at the (t+1)th iteration.

[0066] When satisfied Convergence This is the convergence threshold; a convergence threshold is typically set. This two-layer alternating structure ensures the coordination of optimization within and outside the partition, achieving rapid convergence under low traffic conditions. The system converges to the optimal voltage consistent solution within a finite number of iteration steps, realizing coordinated control of the entire network.

[0067] The optimization results are sent in real time from the control execution module to the photovoltaic inverter and reactive power compensation device, forming a closed-loop voltage control within the zone. The inverter then uses the optimal solution... The system automatically adjusts active and reactive power to achieve autonomous regulation. By executing this process in a rolling cycle, the system can continuously maintain voltage stability under photovoltaic power disturbances, load fluctuations, and topology changes, achieving robust voltage optimization regulation across the entire grid.

[0068] Simulation verification The effectiveness of the method of this invention was verified using a Python simulation platform based on the CIGRE medium-voltage distribution network model. Figure 2The figure illustrates the voltage distribution at distribution network nodes under heavy load and photovoltaic fluctuation conditions. As shown, under no control and traditional local control, the terminal voltage, while not exceeding the limit, is significantly low, indicating insufficient safety margin. In contrast, the method of this invention, through network-wide coordinated optimization, successfully maintains the voltage amplitude of all nodes strictly within the green safety zone of [0.95, 1.05] per-unit values, and the voltage curve is smoother and more stable, fully demonstrating the superior robustness of this method in dealing with uncertain disturbances. Figure 3 As shown, the convergence performance of the method of this invention is illustrated. The red curve in the figure represents the voltage error norm of the boundary node between two adjacent iterations. The results show that as the number of iterations increases, the error decreases exponentially and rapidly, and drops to the set convergence threshold region around the 15th iteration. This proves that the alternating iteration mechanism has extremely high computational efficiency, can achieve consistent convergence of the entire network with low communication overhead, and meets the requirements of real-time voltage regulation.

[0069] This invention first models the stochastic distribution characteristics of photovoltaic (PV) power output using a Gaussian mixture model (GMM), and then completes the grid stability partitioning based on a comprehensive electrical distance that integrates voltage sensitivity and probability distribution differences. On this basis, for voltage exceedance scenarios caused by PV fluctuations, a distributed alternating iterative algorithm based on LinDistFlow is used for regulation and solution. Simulation results intuitively demonstrate the superiority of this method: in terms of voltage distribution, compared to the limitations of traditional local control in completely eliminating exceedances, this invention successfully maintains the voltage of all network nodes within a safe range of 0.95 to 1.05 per-unit values, demonstrating strong robustness; in terms of algorithm performance, the boundary voltage error decreases exponentially with the number of iterations and converges rapidly, verifying that this strategy has efficient real-time coordination capabilities under low communication conditions and can meet the online autonomous operation requirements of active distribution networks.

[0070] Example 2 An electronic device includes a memory and a processor, the memory being used to store a program that supports the processor in executing the robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration as described in Embodiment 1, the processor being configured to execute the program stored in the memory.

[0071] Example 3 A storage medium storing a computer program, which, when executed by a processor, performs the steps of the robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration in Embodiment 1.

[0072] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration, characterized in that, Includes the following steps: S1. Collect power grid operating parameters and establish a node topology matrix as input for voltage sensitivity and power flow Jacobian matrix calculation; S2. Based on historical photovoltaic power samples, a photovoltaic power output probability density model is established using a multidimensional Gaussian mixture model. The model parameters are solved iteratively using the expectation-maximization algorithm. The objective function is the log-likelihood function. When the log-likelihood function converges, the parameter estimation is completed. The optimal number of mixture components is determined using the Bayesian information criterion. S3. Based on the power flow equation of the distribution network, establish the power flow Jacobian matrix, extract the voltage sensitivity sub-matrix, calculate the sensitivity distance between nodes, use Kullback-Leibler divergence to measure the statistical difference of node voltage distribution, and weight and fuse the sensitivity distance between nodes and the statistical difference of node voltage distribution to obtain the comprehensive electrical distance. S4. Using the node comprehensive electrical distance as input, the density peak clustering algorithm is used to calculate the node local density; the minimum distance from each node to a node with a higher density is calculated; the node comprehensive index is calculated based on the node local density and the minimum distance from each node to a node with a higher density; the node with the largest comprehensive index is selected as the partition center; the remaining nodes are assigned to the corresponding center node according to the minimum distance principle, thus forming a robust and stable partition. S5. Establish a joint objective function for minimizing voltage deviation and network loss within each partition. Combining node power flow balance constraints with voltage and power constraints, linearize the power flow equations using the LinDistFlow model, then substitute them into the joint objective function for minimizing voltage deviation and network loss to obtain the optimal power allocation under fixed boundary conditions. S6. Set up virtual nodes at the boundary nodes of the partitions, calculate the injected power of the virtual nodes, and set boundary voltage coordination constraints between adjacent partitions to form the power-voltage coordination equation of the virtual nodes, thus transforming the power exchange relationship between partitions into a controllable variable form. S7. During the iterative process, under the condition of fixed virtual node voltage, solve the objective function of jointly minimizing voltage deviation and network loss to obtain the optimal power allocation for each partition; then correct the virtual node voltage according to the voltage difference between adjacent partitions. When the virtual node voltage converges to the optimal voltage, the coordinated control of the entire network is realized.

2. The robust voltage optimization and control method for distribution networks based on stable partitioning and alternating iteration as described in claim 1, characterized in that, The formula for establishing the photovoltaic power output probability density model using a multidimensional Gaussian mixture model in step S2 is as follows: in, Let M be the probability density function of photovoltaic power, and M be the number of mixed components; The weight of the m-th Gaussian component. and Let be the mean and covariance matrix of the m-th component, respectively, and satisfy . , It is a normal distribution function; The formula for the log-likelihood function is as follows: in, Here is the parameter set of the multidimensional Gaussian mixture model, and k is the number of iterations. These are the parameters of the multidimensional Gaussian mixture model at the (k+1)th iteration. Here are the parameters of the multidimensional Gaussian mixture model at the k-th iteration, and n is the number of samples. For the i-th photovoltaic sample; The formula for determining the optimal number of mixture components using the Bayesian information criterion is as follows: in, Let L be the optimal number of mixture components, L be the maximum likelihood estimate, and n be the sample size.

3. The robust voltage optimization and control method for distribution networks based on stable partitioning and alternating iteration as described in claim 2, characterized in that, The voltage sensitivity sub-matrix mentioned in step S3 is as follows: in, Let be the sensitivity of the reactive power at node j to the voltage at node i. Let be the voltage amplitude at node i. The amount of reactive power injected into node j; The sensitivity distance between the nodes is: in, The sensitivity distance between nodes i and j. Let be the self-sensitivity of node i. Let be the interaction sensitivity of node j with node i; The formula for using Kullback-Leibler divergence to measure the statistical dissimilarity of nodal voltage distribution is as follows: in, The statistical difference in voltage distribution at nodes i and j. and Let i and j be the voltage probability distributions for nodes i and j, respectively.

4. The robust voltage optimization and control method for distribution networks based on stable partitioning and alternating iteration as described in claim 3, characterized in that, The formula for obtaining the comprehensive electrical distance by weighting and fusing the inter-node sensitivity distance and the statistical difference in node voltage distribution as described in step S3 is as follows: in, For comprehensive electrical distance, All are weighted coefficients.

5. The robust voltage optimization and control method for distribution networks based on stable partitioning and alternating iteration as described in claim 4, characterized in that, The formula for calculating the local density of nodes using the density peak clustering algorithm in step S4 is as follows: in, Let be the local density of node i; This is the cutoff distance parameter; The formula for calculating the minimum distance from each node to nodes with a higher density is as follows: in, Let be the distance from node i to the nearest node with a higher density than its own. Let be the local density of node j; The formula for calculating the node comprehensive index is as follows: in, This is a comprehensive indicator for nodes.

6. The robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration as described in claim 5, characterized in that, The objective function for jointly minimizing voltage deviation and network loss in step S5 is as follows: in, Let the objective function be the k-th partition. For reference voltage, Let i be the voltage at node i. These are the weighting coefficients. For branch resistance, For branch current, A robust and stable set of partitions; The node power flow balance constraint is: in, and These represent the active and reactive power injections at node i, respectively. Let i be the set of nodes connected to node i. , Let be the voltage vectors at nodes i and j. For branch admittance; This represents the complex conjugate operation. Represents the imaginary unit; The voltage and power constraints are as follows: in, Let be the minimum threshold voltage at node i. The maximum threshold voltage at node i. Inject a minimum threshold for the reactive power of node i. Inject the maximum threshold for reactive power at node i; The power flow equations are linearized using the LinDistFlow model to obtain the following: in, Let be the active power of branch ij. Let be the reactive power of branch ij. Let be the reactance of branch ij.

7. The robust voltage optimization and control method for distribution networks based on stable partitioning and alternating iteration as described in claim 6, characterized in that, The power-voltage coordination equations for the virtual node in step S6 include: Virtual Node The injection power is: in, and These represent the active and reactive power entering the partition, respectively. and These represent the active and reactive power of the outflowing zone, respectively. The boundary voltage coordination constraints between adjacent partitions are: in, and These are the virtual boundary node voltages of adjacent partitions p and q, respectively. This is the boundary voltage error limit.

8. The robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration as described in claim 7, characterized in that, The formula for correcting the virtual node voltage based on the voltage difference between adjacent intervals in step S7 is as follows: In the formula, t is the number of iterations. Step size factor The voltage difference between adjacent partition boundaries. Let be the virtual node voltage at the t-th iteration. This represents the virtual node voltage at the (t+1)th iteration.

9. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store programs that support the processor in executing the robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration as described in any one of claims 1 to 8, and the processor is configured to execute the programs stored in the memory.

10. A storage medium storing a computer program, characterized in that, When a computer program is run by a processor, it executes the steps of the robust voltage optimization control method for distribution networks based on stable partitioning and alternating iteration as described in any one of claims 1 to 8.

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